# Responsivity

By Mohit Uniyal|Updated : August 26th, 2022

Responsivity plays an important role in enhancing the performance of the photodetector. Photodetectors play a significant role due to diverse applications across the electromagnetic spectrum, such as in short and long-range communication, visible and infrared camera sensors, and biomedical imaging.

In this article, you will learn about responsivity, its derivation, the factors on which it depends, and the typical responsivities of some materials, which will help you understand the relationship between responsivity and wavelength.

## What is Responsivity?

Responsivity is a measure of input-output gain of the detector in a fibre optic system. In the case of a photodetector, it is the measure of electrical output per optical input. Mostly photodetectors are linear functions of input incident power. The responsivity of a photodetector is typically expressed as units of amperes per watt or volts per watt of radiant power.

## Responsivity Formula

It is typically highest in a wavelength region where the photon energy is above bandgap energy, then declining sharply in the bandgap region, where absorption decreases. It can be derived as follows:-

Rλ= IP/P

Where,

• Rλ= Responsivity
• IP = Output Photo Current
• P = Incident Optical Power

Since hυ = Energy of Photon,

P = rp

Where

• rp = Photon flux = P/hυ = Photons/sec

Hence the electron rate comes out to be,

re = ηrp = ηP/hυ

Therefore, the output current is

Ip= eηP/hυ = eηλ/hc = eηλ/1.24

h = Plank’s Constant = 6.63 × 10-34 joule-sec

### Responsivity Unit

The unit of Responsivity is Amperes per watts(A W1) or volts per watts (V W1).

## Responsivity of Typical Photodetectors

The relationship between responsivity and wavelength can be understood from the table below. The unit of wavelength is in nanometers, and the unit of responsivity is ampere per watts.

 Photodetector Wavelength (nm) Responsivity Silicon PN 550-850 0.41-0.7 Silicon PIN 850-950 0.6-0.8 InGaAs PIN 1310-1550 0.85 InGaAs APD 1310-1550 0.80 Germanium 1000-1500 0.70

The photodetector's responsivity depends on the wavelength of incident radiation and the material's bandgap. The below-given diagram shows the responsivity vs wavelength graph. The different range of responsivity is shown: maximum, average, and minimum.

## Responsivity Questions in Gate Exam

Question 1: The quantum efficiency of the photodiode is 50% with a wavelength of 0.90* 10-6. Determine the responsivity of photodiodes.

Question 2: Determine the wavelength of the photodiode having a quantum efficiency of 40% and Responsivity of 0.304 A/W.

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## FAQs on Responsivity

• The responsivity of a silicon photodiode is measured by illuminating the device with a known amount of laser power and then measuring the output voltage developed across a bias resistor. Responsivity is a measure of input-output gain of the detector in a fiber optic system

• Responsivity is the ratio of electrical output from the detector to the input optical power in optical fibre. It is the ratio of input-output gain. If the output current varies proportionally to the input, it is measured as ampere per watt (A/W).

• The responsivity of silicon photodiode is the amount of sensitivity to light is measured. It is defined as the ratio of photodiode output current (Ip) to incident optical power. For enhancing the performance of the photodetector, responsivity plays an important role. Responsivity = (I_P)/P

• Units of responsivity are amperes per watts (A W−1) or volts per watts (V W−1). Responsivity is defined as the ratio of photodiode optical current or voltage to incident optical power. It is represented as given below,

R_λ= (I_P)/P

• Photodiode response time is basically the root mean square sum of the RC time constant arising from series plus load resistances charge collection time and the junction and stray capacitances. The charge collection time is voltage-dependent and is made up of a fast and a slow component.

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